iūliāProposition 7: If there were two triangles of which one angle of the one were equal to one angle of the other, and two of their remaining angles were contained by proportional sides, and lastly, both or neither of the remaining two are less than a right angle, it is necessary for those two triangles to be mutually equiangular between themselves in all their angles.
Proposition 6: All two triangles, among which an angle of the one equals an angle of the other and the sides containing those two equal angles are proportional, are between themselves mutually equiangular.
Proposition 5: Of all two triangles among which every of the sides respecting one another are one proportion, the angles contained by those proportional sides are proved to be mutually equal.
Proposition 4: Of all two triangles of which the angles of one are equal to the angles of the other, the sides respecting the equal angles are proportional.
Proposition 3: If a right line drawn from any of the angles of a triangle to the base cuts that angle by equals, the two parts of that base are to be the same proportion to the remaining sides of the triangle. And if the two parts of the base, which the line drawn from the angle divides, were proportional to the remaining sides of the triangle, that line is necessarily proved to divide the angle by equals.
Proposition 2: If a right line cutting two sides of a triangle were equidistant to the remaining, then it is to cut those two sides proportionally. And if it cuts proportionally, it is necessary for it to be equidistant to the remaining side.
priorly: https://no-outlet.com/@ivlia/116336755502734396
Proposition 1: If there were one altitude of two rectilinear superficies of equidistant sides or of triangles, then either of them will be so much to the other as its base is to the base of the other.
Proposition 25: If there were [four] proportional quantities, and the first of them were the greatest and the last were the least, the first and last accepted together are necessarily understood to be greater than the other two.
nb: book v ends at prop 25 but if you can believe it (& I certainly can!) Campanus addends his interpretation of the material with 9 propositions of his own, which hereafter will be tagged as "Campanean" (as opposed to "Euclidean") geometry.
Proposition 24: If the proportion of the first to second were as third to fourth, and the proportion of the fifth to second were as sixth to fourth, then the proportion of the first and fifth accepted together to the second will be as the sixth and third accepted together to the fourth.
Proposition 23: If there were however many quantities to some others according to their number, of which any two were indirectly proportioned according to the proportion of two from the prior, the proportions will be in equal proportionality.
